Problem: Solve for $x$ and $y$ using elimination. ${-6x-6y = -60}$ ${-5x+5y = 30}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $6$ ${-30x-30y = -300}$ $-30x+30y = 180$ Add the top and bottom equations together. $-60x = -120$ $\dfrac{-60x}{{-60}} = \dfrac{-120}{{-60}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-6x-6y = -60}\thinspace$ to find $y$ ${-6}{(2)}{ - 6y = -60}$ $-12-6y = -60$ $-12{+12} - 6y = -60{+12}$ $-6y = -48$ $\dfrac{-6y}{{-6}} = \dfrac{-48}{{-6}}$ ${y = 8}$ You can also plug ${x = 2}$ into $\thinspace {-5x+5y = 30}\thinspace$ and get the same answer for $y$ : ${-5}{(2)}{ + 5y = 30}$ ${y = 8}$